It sounds like you are developing a robotic manipulator from scratch so I also assume you will be writing software for position control too. Both the design and control depend on not only the dynamics but also the kinematics of your robot.
Kinematics cover the relationships between the joint angles and link lengths (each "arm" is referred to as a link) so that you can determine the position and orientation (as well as velocities and accelerations) along any part of the robot. One method of modeling the kinematics is to break your set of links into the corresponding series of Denavit-Hartenberg parameters. This is not difficult to do, you just have to familiarize yourself with coordinate frames and determine the coefficients for your particular links.
Keep in mind that we are always considering the robot states to be the angles of the joints (or extension of any prismatic joint). Given any set of angles we can then use the kinematics to determine the Cartesian positions of the robot components. Same goes for angular rates to Cartesian velocities and angular accelerations to Cartesian accelerations (of course the velocities and accelerations depend on the angles and rates as well).
To get the torques we then look at the dynamics, where we use the kinematics to model the robot motion and then examine the reaction forces and moments between links based on the inertia of the moving masses. Again, this is not actually too difficult and reduces to a series of free-body diagrams that can be solved in series. The torque on each joint is then simply the moment being applied to it projected onto the joint axis of rotation.
This is known as the computed torque method whereby we prescribe a trajectory for the manipulator joints over time (angles, angular velocities, and angular accelerations) then use the kinematics to determine the Cartesian motion of the joints and finally solve for the reaction torques in the joints. Essentially we are saying "if the manipulator were to perform this motion, what torques will it need to apply through the motors".
When you control the manipulator, you can then input those computed torques for your desired motion and include a layer of feedback control to correct for errors since our model is never perfect. Of course you can use the kinematics and dynamics to approach the problem in different ways, but you'll always need to include them both.
As 50k4 mentioned in the other answer, there are plenty of software packages to help you do this. However, you will most definitely have to understand the underlying principles in order to translate your particular design into the configuration that the software expects (i.e., DH parameters or some other accepted convention). Manipulators can be a bit daunting so take it in stride!